A Hitchhiker's Guide to Scaling Law Estimation (2410.11840v1)

Abstract: Scaling laws predict the loss of a target machine learning model by extrapolating from easier-to-train models with fewer parameters or smaller training sets. This provides an efficient way for practitioners and researchers alike to compare pretraining decisions involving optimizers, datasets, and model architectures. Despite the widespread use of scaling laws to model the dynamics of LLM training, there has been little work on understanding how to best estimate and interpret them. We collect (and release) a large-scale dataset containing losses and downstream evaluations for 485 previously published pretrained models. We use these to estimate more than 1000 scaling laws, then derive a set of best practices for estimating scaling laws in new model families. We find that fitting scaling laws to intermediate checkpoints of training runs (and not just their final losses) substantially improves accuracy, and that -- all else equal -- estimates of performance are generally most accurate when derived from other models of similar sizes. However, because there is a significant degree of variability across model seeds, training multiple small models is sometimes more useful than training a single large one. Moreover, while different model families differ scaling behavior, they are often similar enough that a target model's behavior can be predicted from a single model with the same architecture, along with scaling parameter estimates derived from other model families.

Overview of "A Hitchhiker's Guide to Scaling Law Estimation"

The paper "A Hitchhiker's Guide to Scaling Law Estimation" by Choshen, Zhang, and Andreas examines the estimation and interpretation of scaling laws in machine learning, particularly focusing on LLMs. It provides a comprehensive analysis of scaling laws, which are crucial for extrapolating the performance of target models from smaller, more manageable models.

Key Contributions

The research introduces a large-scale dataset that includes losses and downstream evaluations for 485 pre-trained models. Using this data, the authors estimate over 1000 scaling laws, deriving best practices for effectively estimating scaling laws across different model families.

The paper investigates the following key aspects:

1. Extrapolation Reliability:
   • The paper highlights the variability caused by different random parameter initializations, suggesting that improvements can result in loss changes from 4% to 50%. This provides crucial insights into how reliably scaling laws can be expected to predict outputs.
2. Variation Across Families:
   • Different model families show distinct scaling behavior, yet they can often be similar enough to allow for performance prediction of a target model using data from another model family.
3. Intermediate Checkpoints:
   • Contrary to conventional practices of using fully trained models, the paper finds that estimating scaling laws using intermediate training checkpoints significantly improves prediction accuracy.
4. Model Size Dependency:
   • While larger models provide generally more accurate estimates, the paper suggests that training multiple smaller models can offer better predictive accuracy due to reduced variance.
5. Cost-effective Estimation:
   • The authors chart out a strategy for cost-effective scaling law estimation, balancing the number of models, their sizes, and the number of training tokens.

Numerical Results and Implications

The research demonstrates strong numerical results, with scaling laws achieving an average absolute relative error (ARE) of 4%. This level of precision is validated as the minimal effect size that is typically meaningful in improving model performance, based on previous literature.

The implications of these findings are significant in both theoretical and practical dimensions. Theoretically, the paper informs a more nuanced understanding of scaling behaviors, suggesting that the commonly used functional form of scaling laws may have fewer degrees of freedom. Practically, the results can guide more efficient decision-making in LLM training, reducing unnecessary computational expenditure by advising on optimal small-scale experiments prior to full-scale model training.

Future Directions

Future work could explore improved parameterizations of scaling laws, factoring in additional aspects such as learning rate schedules. There's also potential in expanding the dataset and further examining cross-family predictions. This paper sets a foundation for such exploration, providing a toolbox for current and future researchers to refine and optimize ML model training processes.

In conclusion, "A Hitchhiker's Guide to Scaling Law Estimation" presents a methodically rich examination of scaling laws, offering significant contributions to understanding their estimation and application. This paper stands as a valuable resource for researchers and practitioners aiming to optimize LLM training and evaluation.